A uniform beam HK of length \(10 \mathrm{~m}\) and weighing \(200 \mathrm{~N}\) is supported at both ends. A man weighing, \(100 \mathrm{~N}\) stands at a point \(P\) on the beam. if the reactions at \(\mathrm{H}\) and \(\mathrm{K}\) are respectively \(800 \mathrm{~N}\) and \(400 \mathrm{~N}\), then the distance HP is ____________

A. \(4 \mathrm{~m}\)
B. \(3 \frac{1}{3} \mathrm{~m}\)
C. \(3 m\)  
D. \(6 \frac{2}{3} \mathrm{~m}\)
E. \(7 \mathrm{~m}\)

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Correct Answer: C